White House Chief of Staff Mark Meadows , speaking to reporters on Air Force One on the flight that carried President Donald Trump to a campaign rally in Wisconsin, said he would not identify the five nations.
But he said three were in the region. He would not comment further.
Trump has spoken about more countries agreeing to a normalization of relations with Tel Aviv following Abu Dhabi and Manama deals.
One possibility is Oman, Reuters reported, noting that the Omani ambassador attended the White House ceremony on Tuesday. Trump, earlier on Tuesday, predicted that Saudi Arabia would eventually agree to a deal.
The Times of Israel reported earlier this week that other Arab countries believed to be close to recognizing Israel include Oman, Sudan and Morocco.